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Unfortunately, your photos did not come through. I am unable to see the damage. You did mention that it is on the east side of your house, which would give less sun if you have the shade from the house on it. This might leave the soil a little more moist. This can cause root rot. Some species of root rot will have a smell to them. You might try and confirm that there is a smell, though this isn't a good way to test for rot. Many do not smell strongly.

This article will offer information on the treatment, and prevention, as well as testing information:

https://www.gardeningknowhow.com/plant-problems/disease/root-rot-in-garden-plants.htm

Dead or diseased limbs can be removed at any time, so if those limbs are dead, they can be removed now. Save the height reduction till when the plant is dormant. (See the varieties below for best time to prune.) You also might consider removing the trees and replacing them with a shrub that won't need height reduction. These articles should help:

https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-scratch-test.htm

https://www.gardeningknowhow.com/ornamental/shrubs/holly/trimming-holly-bushes-how-to-prune-holly-bushes.htm

https://www.gardeningknowhow.com/garden-how-to/info/pruning-evergreens.htm

https://www.gardeningknowhow.com/ornamental/shrubs/holly/holly-winter-care.htm

https://www.gardeningknowhow.com/ornamental/shrubs/holly/leaf-scorching-in-holly.htm

https://www.gardeningknowhow.com/ornamental/shrubs/holly/growing-holly-bushes.htm

https://www.gardeningknowhow.com/ornamental/shrubs/shgen/evergreen-garden-shrubs.htm

https://www.gardeningknowhow.com/garden-how-to/design/lideas/foundation-plant-spacing.htm

Unfortunately, your photos did not come through. I won't be able to give you a precise answer. There are many things that cause these symptoms, so narrowing them down can be difficult. First, and foremost, you will want to test nutrient levels and pH levels of your soil. If those come back good, then a fungicide may be in order. Infections are common after rainy seasons, so if your soil remains too wet, then it can invite infection suffocate roots. Hollies tend to be more drought resistant than water logged soil resistant. One last thing to consider will be pests. I would inspect the area for insects. They can be a problem that leads to infection and damage.

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/test-soil-for-pests-and-diseases.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/soil-ph-plants.htm

https://www.gardeningknowhow.com/garden-how-to/soil-fertilizers/testing-soil.htm

https://www.gardeningknowhow.com/garden-how-to/info/using-fungicides-in-garden.htm

https://www.gardeningknowhow.com/ornamental/shrubs/holly/growing-holly-bushes.htm

Unfortunately, your photos did not come through. I am unable to see the growth. This should resemble the rest of the shrub. It could be a sucker from the root stock, if it is a grafted specimen. This is most likely, actually. Keep those that grow from the base pruned away, and look for growth that resembles your shrub.

https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-sucker-removal-and-tree-sucker-control.htm

https://www.gardeningknowhow.com/ornamental/shrubs/holly/growing-holly-bushes.htm

If the plant was grafted, and the new growth is coming from below the graft, then whatever shrub is produced will not look the same as the top growth. If you still have the tag or know the cultivar name, you can find out if it is grafted.

If it isn't, then just the top growth died back and new shoots are coming back from the roots. You don't need to be in a hurry to cut it back. Wait and see if more leaves reemerge further up the stalk. (I have a plant that does this after winter dieback.) I suggest waiting till its dormant in late winter to do any pruning.

https://www.gardeningknowhow.com/ornamental/shrubs/holly/trimming-holly-bushes-how-to-prune-holly-bushes.htm

https://www.gardeningknowhow.com/ornamental/trees/tgen/what-is-a-graft-collar.htm

Thank you for sending us your gardening question.

Holly will accept severe pruning and it will grow back. It is best to do renewal pruning in late winter. Afterwards, you can keep it in check with regular pruning. Or, remove the trees and replace them with a plant that will mature at the height you want; thereby reducing pruning chores.

https://www.gardeningknowhow.com/ornamental/shrubs/holly/trimming-holly-bushes-how-to-prune-holly-bushes.htm